Analytical solution for groundwater flow and drawdown when pumping from a mixed confined-unconfined aquifer

When groundwater is pumped from a confined aquifer, severe drawdown can lower the hydraulic head below the aquifer top. This causes a local transition to unconfined conditions. This paper presents a simple analytical equation to calculate steady-state flow to a fixed-head pumping well within a mixed confined-unconfined aquifer system. The developed solution applies to steady-state conditions with a constant pumping rate from a single fixed-head, fully penetrating borehole in a semi-infinite domain, and where the hydraulic head is fixed at the distant radius of influence. Additional conditions include level and constant aquifer boundaries, together with the Dupuit-Forchheimer assumption, which dictates horizontal groundwater flow in the unconfined zone proportional to the saturated thickness. This mathematical solution successfully calculates the lowered hydraulic head at a radial distance from the well, across both the unconfined domain and the artesian pressure confined aquifer domain. Findings demonstrate that for a fixed head pumping well, the drawdown for a mixed confined-unconfined condition falls predictably between the extremes of fully confined or unconfined systems. Finally, the analytical solution developed was verified against simulations from a mixed confined-unconfined Finite Element Model for both drawdown and abstraction rates, and showing precise agreement with the Girinskii potential function.